PRP Records

Probable Primes Top 10000

(292102 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 50000) Who ? When ?
60012^344309-1852033103648Enzo Doria08/2015
600225729^10672+10672^25729103643Hans Havermann09/2020
6003(2^344289+1166)/2103642Stefano Morozzi09/2020
60043*10^103637+61103638Robert Price09/2020
6005(2^344246+1614)/2103629Stefano Morozzi09/2020
60062^344213-21253103619Enzo Doria06/2013
60072^344196-465103614Lelio R Paula11/2016
60082^344187-20001103611Enzo Doria06/2013
6009(117191#+(355573#)/(117191#))/(200233679)103602Makoto Morimoto10/2017
6010(237^43627-1)/236103601Serge Batalov06/2022
601120^79621-19^79621103590Jean-Louis Charton03/2011
6012Phi(155391,10)/1243129103586Maksym Voznyy09/2015
60132^344085-20365103580Enzo Doria06/2013
60145^148169+54103566Lelio R Paula11/2016
60152^344017-108795103560Enzo Doria03/2014
6016(2^343974+2670)/2103547Stefano Morozzi09/2020
60172^343971-5077103546Lelio R Paula09/2011
6018(7*10^103531+71)/3103532Robert Price05/2018
60192^343899+141103524Lelio R Paula08/2011
6020(2^343933+1)/(3*98294339989393)103520Gord Palameta08/2018
60216^133029-67103517Lelio R Paula11/2016
6022(17*2^343877+1)/13625103515Lelio R Paula12/2013
602366*10^103507+7103509Robert Price07/2020
602426297^8614+8614^26297103485Hans Havermann09/2020
6025(2^343764+2658)/2103483Stefano Morozzi09/2020
602626499^8036+8036^26499103480Hans Havermann09/2020
6027(136*10^103474-1)/9103476Serge Batalov12/2014
60285^148014-24103458Lelio R Paula11/2016
602928316^4503+4503^28316103453Hans Havermann09/2020
6030(22*10^103450+53)/3103451Robert Price07/2019
60312^343604+9931103436Yves Minet01/2011
60322^343601-21189103435Enzo Doria06/2013
6033(10^103423+173)/3103423Robert Price05/2021
60342^343508-115229103407Enzo Doria06/2015
6035(8766^26227-1)/8765103404Serge Batalov06/2022
6036(509203*2^343491-1)/16147103403Lelio R Paula05/2015
60373^216685-113056103386Enzo Doria07/2014
603824829^14580+14580^24829103382Hans Havermann08/2020
603991355!4+1024103381Robert Price09/2019
604044^62903-43^62903103379Jean-Louis Charton08/2012
604111^99262-20103371Lelio R Paula12/2016
6042(509203*2^343357-1)/5103366Lelio R Paula05/2015
6043(2^343363+3570)/2103363Stefano Morozzi09/2020
60442^343356-2791889103361Enzo Doria03/2016
6045(25*10^103360-241)/9103361Robert Price05/2018
6046Phi(104989,10)/2939693103350Maksym Voznyy09/2015
604724826^14511+14511^24826103319Hans Havermann09/2020
60482^343182-171103309Lelio R Paula08/2011
6049(23619^23619+23620^23620)/7187103294David Broadhurst09/2009
6050(10680^25639-1)/10679103285Serge Batalov06/2022
6051(7427^26683-1)/7426103282Serge Batalov06/2022
60522^343079-1835611103278Enzo Doria05/2015
60532^343063-1147103273Yves Minet06/2013
605424741^14930+14930^24741103271Hans Havermann09/2020
6055(16*10^103255-73)/3103256Robert Price07/2020
6056(219^44119-1)/218103256Serge Batalov06/2022
60579*6^132689+7103254Lelio R Paula11/2014
60582^342979-18085103247Enzo Doria05/2013
6059(16*10^103244-31)/3103245Robert Price03/2019
60602^342966-16995103244Lelio R Paula11/2016
606123797^21774+21774^23797103230Hans Havermann09/2020
606225388^11637+11637^25388103224Hans Havermann09/2020
6063(2^342876+2086)/2103216Stefano Morozzi09/2020
6064(16*10^103214-31)/3103215Robert Price03/2019
6066(37*10^103211+611)/9103212Robert Price11/2018
6065(238*10^103210-1)/3103212Robert Price04/2020
60675^147650+16103203Lelio R Paula11/2016
6068gcd(Phi(852060,10),(10^42603+1)^3*(10^42603+1-10^21302)+(10^85206+10^42603)*(10^21302+1)+10^127809)103201Serge Batalov04/2015
60692^342817+2707067103199Enzo Doria03/2016
607043^63177-42103198Theodore Burton02/2007
60712^342805-21025103195Enzo Doria06/2013
607224129^18890+18890^24129103182Hans Havermann09/2020
6073(622*10^103171-1)/9103173Robert Price11/2021
60742^342714+12285103168Lelio R Paula11/2016
6075(2*10^103161-17)/3103161Serge Batalov11/2022
607618^82178-4481103156Enzo Doria03/2013
60772^342665-17349103153Enzo Doria05/2013
607830408^2467+2467^30408103150Hans Havermann09/2020
6079(5^147571-3^147571)/2103148Kellen Shenton05/2022
6080(2^342615+3090)/2103138Stefano Morozzi09/2020
60812^342612+175103137Lelio R Paula08/2011
60825*2^342585-3103130Lelio R Paula09/2014
6083(16*10^103127+77)/3103128Robert Price03/2019
6084(2^342527+3774)/2103111Stefano Morozzi02/2021
60852^342503-19209103104Enzo Doria05/2013
6086(2^342484+2586)/2103098Stefano Morozzi09/2020
60872^342476+51103096Lelio R Paula08/2011
60882^342460-18885103091Enzo Doria05/2013
6089(2^342442+862)/2103086Stefano Morozzi02/2021
6090(194*10^103074-17)/3103076Robert Price09/2020
60917^121968+82103075Lelio R Paula10/2016
60922^342392-108863103071Enzo Doria03/2014
6093(2^342389+806)/2103070Stefano Morozzi01/2021
60943^216014+28103065Lelio R Paula11/2016
60952^342353-108879103059Enzo Doria03/2014
609610^103055+276081103056Patrick De Geest12/2016
609710^103055-53103055Lelio R Paula11/2016
6098(58*10^103046+419)/9103047Robert Price05/2019
60997^121933+4103046Lelio R Paula11/2014
6100(71*10^103028-143)/9103029Robert Price10/2021
6101(2^342235+3618)/2103023Stefano Morozzi09/2020
610219^80560-68103017Lelio R Paula10/2016
61032^342209+76607103016Enzo Doria05/2016
6105328^40945+40945^328103013Norbert Schneider12/2014
610412^95454-91103013Lelio R Paula10/2016
610625833^9716+9716^25833103009Hans Havermann01/2019
6107(893*10^103004+7)/9103006Robert Price06/2021
6108(1475^32503-1)/1474102993Serge Batalov06/2022
610965^56809-64^56809102990Robert Price08/2013
61105^147338-6102985Lelio R Paula11/2014
61112^342084-112739102978Enzo Doria06/2014
61129*6^132330+7102974Lelio R Paula11/2014
61132^342034-16737102963Enzo Doria05/2013
6114(9787*2^342011-1)/25102959Lelio R Paula05/2015
6115(3^215802-5)/124343756102956Lelio R Paula12/2013
61162^341991-17421102950Enzo Doria05/2013
61172^341969-112225102943Enzo Doria06/2014
6118(9787*2^341864-1)/3102915Lelio R Paula05/2015
61192^341859+1869413102910Enzo Doria05/2016
612010^102909+61102910Lelio R Paula11/2016
612110^102909-67049102909Patrick De Geest12/2016
612223814^20935+20935^23814102898Hans Havermann02/2019
612328345^4264+4264^28345102888Hans Havermann02/2019
612425665^10204+10204^25665102886Hans Havermann02/2019
612526288^8181+8181^26288102860Hans Havermann02/2019
61262^341659+1836773102850Enzo Doria03/2016
61272^341608-110639102835Enzo Doria05/2014
612810^102824+49102825Lelio R Paula11/2016
612910^102824-168011102824Patrick De Geest12/2016
613011^98708-8102794Lelio R Paula10/2016
61312^341466+4429102792Lelio R Paula09/2011
61322^341460-107102790Lelio R Paula08/2011
6133(2^341388+47)/21014943102761Lelio R Paula12/2013
61342^341355+21102759Lelio R Paula08/2011
6135(6496^26947-1)/6495102736Serge Batalov06/2022
61362^341246+40755102726Lelio R Paula11/2016
6137(2^341256-5)/991699102723Lelio R Paula12/2013
61387^121547+78102720Lelio R Paula10/2016
61392^341223-461197102719Enzo Doria06/2015
614027838^4893+4893^27838102711Hans Havermann03/2019
61422^341190-20577102709Enzo Doria06/2013
6141(27*2^341212+1)/84674449102709Lelio R Paula12/2013
6143(25*10^102698+77)/3102699Robert Price09/2022
61446^131976-65102698Lelio R Paula10/2016
61452^341134+2533102692Henri Lifchitz09/2005
614613^92184-54102688Lelio R Paula10/2016
61472^341116-20873102687Enzo Doria06/2013
61482^341094-19953102680Enzo Doria06/2013
614923761^20950+20950^23761102676Hans Havermann03/2019
61512^341053+129102668Lelio R Paula08/2011
6150(4724^27943-1)/4723102668Serge Batalov06/2022
6153(31*2^341006-1)/3102655Lelio R Paula03/2014
61527^121471+94102655Lelio R Paula10/2016
61552^341004-173102653Lelio R Paula08/2011
615420^78901+3102653Lelio R Paula10/2016
6156(2^341001+1674)/2102652Stefano Morozzi09/2020
61575^146853-52102646Lelio R Paula10/2016
61582^340969-216931102642Enzo Doria05/2014
6159122^49196+121102641Norbert Schneider10/2018
61602^340952+1870021102637Enzo Doria05/2016
61615*2^340940-3102634Lelio R Paula08/2014
6162(6^131891+1)/7102631Paul Bourdelais01/2010
6163(11*10^102629-23)/3102630Robert Price09/2021
616425876^9239+9239^25876102615Hans Havermann02/2019
6165(4*10^102612+83)/3102613Robert Price02/2018
616675^54717+74102598Norbert Schneider01/2015
6167(17*10^102597+13)/3102598Robert Price01/2019
61682^340806-20393102593Enzo Doria06/2013
6169(2^340790+5)/138267102583Lelio R Paula12/2013
61706^131821+77102577Lelio R Paula10/2016
6171(203*10^102561-11)/3102563Robert Price12/2020
61722^340688-29102558Henri Lifchitz05/2005
61732^340685-109101102557Enzo Doria04/2014
617465^56567-64102552Norbert Schneider11/2014
617526230^8121+8121^26230102550Hans Havermann03/2019
6176(64*10^102547+161)/9102548Robert Price08/2022
6177(8*10^102541+49)/3102542Robert Price05/2020
6178(536*10^102533-23)/9102535Robert Price02/2020
61792^340547-108897102515Enzo Doria03/2014
6180(2^340536+778)/2102512Stefano Morozzi09/2020
618125592^10119+10119^25592102500Hans Havermann02/2019
6182(5*10^102492-23)/9102492Serge Batalov11/2022
61837^121268+82102484Lelio R Paula10/2016
6184(6883*2^340443-1)/162401102483Lelio R Paula05/2015
61852^340434-5955102481Lelio R Paula11/2016
6186(7*10^102480-19)/3102481Robert Price10/2020
6187(2^340381+47)/7102465Lelio R Paula12/2013
6188111^50095+110102461Norbert Schneider04/2017
61892^340291-20301102438Enzo Doria06/2013
619012^94915+89102431Lelio R Paula10/2016
6191(106*10^102422+17)/3102424Robert Price04/2021
619224466^15349+15349^24466102417Hans Havermann03/2019
61932^340212+111546435102415Paul Bourdelais10/2021
61942^340208-20373102413Enzo Doria06/2013
61956^131598-17273102404Enzo Doria02/2013
6196(2^340132+1182)/2102390Stefano Morozzi09/2020
6197(2^340133+1166)/2102390Stefano Morozzi09/2020
61982^340115-21181102385Enzo Doria06/2013
6199(55459*2^340090+1)/1591102379Lelio R Paula07/2014
6200(2^340064+3630)/2102370Stefano Morozzi09/2020
620189^52511-88^52511102365Robert Price06/2015
62023^214539-112756102362Enzo Doria07/2014
620323159^23450-23450^23159102353Norbert Schneider12/2019
62042^340000-19877102351Enzo Doria06/2013
62052^339990-114845102348Enzo Doria05/2015
6206(3^214516-2)/51383102346Lelio R Paula12/2013
620720^78661-99102341Lelio R Paula09/2016
62082^339951-19585102336Enzo Doria05/2013
6209(17*10^102335-167)/3102336Robert Price05/2022
6210(13*2^339943+1)/45102333Lelio R Paula12/2013
6211(236282#+121441)/(121441*25499429)102332Makoto Morimoto08/2020
62125*10^102323-91102324Robert Price03/2021
62142^339889+29327102317Yves Minet06/2010
6213(167*10^102315-17)/3102317Robert Price03/2020
621526348^7641+7641^26348102314Hans Havermann03/2019
6216Phi(239414,10)/6333218543102303Makoto Kamada08/2019
62172^339834-109493102301Enzo Doria04/2014
6218(16*10^102299-19)/3102300Robert Price02/2019
6219(11^98221-5^98221)/6102286Robert Price01/2013
62203^214365+1820102279Lelio R Paula10/2016
622131978^1579+1579^31978102278Hans Havermann03/2019
6222(89*10^102262-467)/9102263Robert Price04/2022
6223(11*2^339705-1)/183102261Lelio R Paula03/2014
62242^339694-16995102259Lelio R Paula09/2016
6225(56*10^102255+691)/9102256Robert Price05/2019
6226122^49008+121102249Norbert Schneider10/2018
6227(2^339652+3178)/2102246Stefano Morozzi09/2020
62287^120985-38102245Lelio R Paula10/2016
622910^102244+122961102245Patrick De Geest12/2016
623010^102244-27102244Lelio R Paula09/2016
62317^120982-62102242Lelio R Paula10/2016
6232(2^339640+2670)/2102242Stefano Morozzi09/2020
62334*6^131382-5102236Lelio R Paula11/2014
6234(2^339607+3290)/2102232Stefano Morozzi02/2021
62352^339586-1091102226Yves Minet11/2012
623611^98161-3072000102225Enzo Doria12/2012
62379*7^120961-4102225Lelio R Paula11/2014
62385*3^214250+2102224Serge Batalov10/2010
623912^94713-59102213Lelio R Paula10/2016
624012^94705+89102204Lelio R Paula10/2016
62412^339407-177102172Lelio R Paula08/2011
62424*10^102163-57102164Robert Price10/2018
62432^339355+65102157Lelio R Paula07/2011
6244(28*10^102142-31)/3102143Robert Price12/2019
6245(2^339323+47)/880715102141Lelio R Paula12/2013
6246(2^339268+1758)/2102130Stefano Morozzi09/2020
6247s(178551)102122Robert Price05/2020
6248(797*10^102112-23)/9102114Robert Price01/2022
6249(5*10^102107+7)/3102108Tyler Busby02/2023
6250(2^339175+2790)/2102102Stefano Morozzi02/2021


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 20 2023 09:01 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!